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A110104 a(n) is the number of coverings of 1..n by cyclic words of length 3n, such that each value from 1 to n appears precisely twice. That is, the union of all the letters in all of the words of a given covering is the multiset {1,1,2,2,...,n,n}. No repeats of words are allowed in a given covering. 3
1, 4, 3760, 23504320, 567399078400, 37518268781593600, 5543744611870143078400, 1599334510537656091623424000, 818296434784062385011283591168000 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

P-recursive.

LINKS

Table of n, a(n) for n=0..8.

FORMULA

Differential equation satisfied by egf: sum a(n)t^3n/(3n!) {F(0) = 1, (-2+4*t^6+16*t^3)*(d/dt)F(t) + 4*t^4*(d^2/dt^2)F(t) + t^2*(4+12*t^3+t^6)*F(t)}.

Recurrence: {a(0) = 1, (40320 + 328752*n + 1816668*n^3 + 1102248*n^5 + 398034*n^6 + 1818369*n^4 + 1063116*n^2 + 78732*n^7 + 6561*n^8)*a(n) +(508608*n + 161280 + 453600*n^3 + 34992*n^5 + 2916*n^6 + 173340*n^4 + 661104*n^2)*a(n+1) + (12320 + 19980*n + 12096*n^2 + 3240*n^3 + 324*n^4)*a(n+2) - 2*a(n+3), a(1) = 4, a(2) = 3760}.

EXAMPLE

a(1)=4: {123, 132} {112, 233} {113, 322} {133, 122}

CROSSREFS

Cf. A052502, A110105, A110106, A108242.

Sequence in context: A114498 A069120 A221191 * A024061 A013830 A320860

Adjacent sequences:  A110101 A110102 A110103 * A110105 A110106 A110107

KEYWORD

easy,nonn

AUTHOR

Marni Mishna, Jul 11 2005

STATUS

approved

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Last modified June 21 16:29 EDT 2021. Contains 345365 sequences. (Running on oeis4.)